Question

Somebody please help me! I have spent the past 5 hours on this problem and so far nobody can help me. I don't understand any of this!
Calculate the consumers' surplus at the indicated unit price (P Bar) for the demand equation
q=20-0.05p^2; (P Bar=2)

Answer 1

here is an example

Answer 2

any clue? :/

Answer 3

Hello, Alec,

I did an Internet search for "consumer's surplus" and came up with the following: http://en.wikipedia.org/wiki/Economic_surplus.

There I see that the "consumer's surplus" is the area beneath the demand curve and above the equilibrium price (which in this problem is apparently p bar). Once that is understood, this math problem boils down to finding the numeric value of this area.

I trust you're familiar with using definite integrals to determine areas.

Note that q = 20 - 0.05p^2 can be solved for p: p = Sqrt(400-20q).

I'll divide the red area (shown in http://en.wikipedia.org/wiki/Economic_surplus) into thin vertical strips of width dq. The upper bound on each such strip is p = Sqrt(400-20q). The lower bound is p bar (which is 2 in this problem statement). Thus, we need to integrate [Sqrt(400-20q) - 2]dq from q = 0 to q = 19.8.

Alternatively, let's not solve q = 20 - 0.05p^2 for p, but use it as is, representing the right end of horizontal (instead of vertical) strips subdividing the red area in http://en.wikipedia.org/wiki/Economic_surplus. We'll need to integrate [(20 - .05p^2) - 2) dp from p = 2 (this is the value of p bar) to p = 20 (this is the p value at which q = 0). This integral is much simpler than the previous one!

Integrating, I get [20p - 0.05(p^3)/3 - 2p] with upper limit p = 20 and lower limit p = 2. I obtain this result: consumer's surplus = $190.80.

Answer 4

Please ask questions about anything that is not clear to you in this discussion. Good luck!

Answer 5

I typed it in and its incorrect :P

Answer 6

I'm so glad. But be certain that you can set up and solve this problem yourself. Again, ask any questions you like that would lead to bettering your understanding of the process. I'm logging off now, but you could, if you wished, send me a mail message through openstudy.com.